A071007 - OEIS

%I #9 Jun 14 2015 18:58:06

%S 0,0,0,2,8,40,200,980,5152,28448,162080,979000,6179360,40575392,

%T 279199648,1997406320,14825619200,114365751040,912510870272,

%U 7521873125408,64045101880960,561615674345600,5067769601121920,47023128008540992,447820056115824128

%N Number of permutations in the symmetric group S_n such that the maximal cycle has length exactly 3.

%C E.g.f.: exp( x + (x^2)/2 + (x^3)/3 ) - exp( x + (x^2)/2 ).

%H Alois P. Heinz, <a href="/A071007/b071007.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = A057693(n) - A000085(n).

%t nn=20;Range[0,nn]!CoefficientList[Series[Exp[x+x^2/2+x^3/3]-Exp[x+x^2/2],{x,0,nn}],x]  (* _Geoffrey Critzer_, Jan 23 2013 *)

%o (PARI) for(n=0,25,print1(polcoeff(serlaplace(exp(x+x^2/2+x^3/3)-exp(x+x^2/2)),n)","))

%Y Cf. A057693, A000085, A027617.

%Y Column k=3 of A126074.

%K nonn

%O 0,4

%A Sharon Sela (sharonsela(AT)hotmail.com), May 19 2002

%E More terms from _Ralf Stephan_, Apr 09 2003